Perimeter = the sum of the lengths of all the sides[2] X Research source Apothem = a segment that joins the polygon’s center to the midpoint of any side that is perpendicular to that side[3] X Research source
Think of the apothem as being the “x√3” side of a 30-60-90 triangle. You can think of it this way because the hexagon is made up of six equilateral triangles. The apothem cuts one of them in half, creating a triangle with 30-60-90 degree angles. You know that the side across from the 60 degree angle has length = x√3, the side across from the 30 degree angle has length = x, and the side across from the 90 degree angle has length = 2x. If 10√3 represents “x√3,” then you can see that x = 10. You know that x = half the length of the bottom side of the triangle. Double it to get the full length. The bottom side of the triangle is 20 units long. There are six of these sides to the hexagon, so multiply 20 x 6 to get 120, the perimeter of the hexagon.
area = 1/2 x 120 x 10√3 area = 60 x 10√3 area = 600√3
If you have a triangle with a base of 10 and a height of 8, then the area = 1/2 x 8 x 10, or 40.
If the square has a side length of 6, then the area is 6 x 6, or 36.
If the base of the rectangle is 4 and the height is 3, then the area of the rectangle is 4 x 3, or 12.
Let’s say you have a trapezoid with bases that have a length of 6 and 8 and a height of 10. The area is simple [(6 + 8) x 10]/2, which can be simplified to (14 x 10)/2, or 140/2, which makes for an area of 70.
